MIT 18.01 Single Variable Calculus: Topics, Study Guide, Practice

MIT 18.01 is MIT's first-semester calculus subject, part of the Calculus I General Institute Requirement. It covers single-variable calculus from the first derivative to power series in one term, which is more ground than most Calculus 1 courses elsewhere. This guide maps every 18.01 topic to free practice, so you can learn each idea by solving problems with instant feedback.

What MIT 18.01 covers

According to the MIT course catalog, 18.01 covers differentiation and integration of functions of one variable, with applications to geometry and science. It then goes further than a typical Calculus 1 course, adding techniques of integration, polar coordinates, L'Hôpital's rule, improper integrals, and infinite series including power series.

In practice, that means 18.01 spans two courses at many other universities: all of Calculus 1 and the first half of Calculus 2.

18.01 topic map

Each row links to a lesson you can practice and to a reference page or guide that explains the idea.

18.01 vs 18.01A vs 18.02

18.01 and 18.01A both satisfy Calculus I and exclude credit for each other. If you took a strong high school calculus course, 18.01A lets you spend most of your time on integration techniques, improper integrals and series. See the MIT 18.02 guide for what comes next.

Example problems at the 18.01 level

These three problems show the range of the course, from a first derivative to a series.

1. A chain rule derivative. Differentiate y = \sin(x^2).

2. Integration by parts. Evaluate \int x e^x\,dx with u = x and dv = e^x\,dx:

3. A convergent improper integral.

How to do well in MIT 18.01

• Practice every day in short sessions. The course covers a lot in one term, and skills like the chain rule only become automatic through repetition.
• Fix algebra slips early. Most lost points come from algebra and sign errors, not calculus. Our list of common calculus mistakes covers the big ones.
• Keep the formulas in front of you. The calculus formula sheet has every derivative and integral on one page.
• Test yourself under time pressure before each exam, using practice exams with fresh numbers every time.

Tip: if series feel abstract at first, start with the geometric series formula. Almost every convergence argument in 18.01 builds on it.